This achievement is very easy... first, I struggled to make a headshot kill with Golden Harbinger (melee weapon) but it's pretty easy after accidentally finding a trick to grind. First.. you will get this weapon by killing "Gergis the Herald" during the DLC mission. Just you need to equip this weapon on any slot and during combat, get a headshot with a bow while your health is a bit low and it'll count towards the achievement. Even animal kills also count towards progression. Get 10 headshot kills and Achievement will POP.
UPDATE:
1. Civilian kills also counts towards the achievement, which will progress faster to get this achievement.
2. You can have full health during kills, no need to get hurt, and regenerate health through kills to progress towards the achievement.
UPDATE 1: Thanks to Basement Cheese and LLboxed
As Basement Cheese told YOU can be at full HEALTH while hitting headshot, So no healing stuff is needed for this achievement.
UPDATE 2: Thanks to JeroenRos and SweptbackFlame
JeroenRos and SweptbackFlame added more easy ways to get headshot kills... you can headshot civilians with the bow and it counts as kills towards achievement.
SweptbackFlame commented that "Once you get the weapon if you go straight to the Smoke and Fury mission, you can just headshot civilians with the bow. They count as kills. There are tons of civilians you can headshot and they don't even move."
This method is faster to grind kills for this achievement.